If the rivet is going to be against something (clothes, animal,ect.) I'll put the flat side against the object. So it doesn't rub on it. The burr should face which ever direction so it doesn't rub on person or object. To peen the rivet I cut the stud off a little above the washer after I set it and take a hammer and wack the stud a couple of times to flatten it out. I'll then take the doming tool and dome it. There's another tool(dont know the name) that's round and slightly concave and should be used to hit the flat head of the rivet with after doming the stud. It makes the head of the rivet convex. And therefore leaving a nice smooth surface.
Mike